Trig without Tears

or, How to Remember Trigonometric Identities

revised 13 Jun 2006
Copyright © 1997–2007 Stan Brown, Oak Road Systems

Summary: Faced with the large number of trigonometric identities, students tend to try to memorize them all. That way lies disaster. When you memorize a formula by rote, you have no way to know whether you’re remembering it correctly. I believe it is much more effective (and, in the long run, much easier) to understand thoroughly how the trig functions work, memorize half a dozen formulas, and work out the rest as needed. That’s what these pages show you how to do.

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Contents:

Introduction: About Trigonometry | About Trig without Tears | Notation

The Six Functions: The Basic Two: Sine and Cosine | The Other Four: Tangent, Cotangent, Secant, Cosecant | Six Functions in One Picture | Why Call It Sine?

Functions of Special Angles: Functions of 45° | Functions of 30° and 60° | Mnemonic for All Special Angles

Functions of Any Angle: Not Just Triangles Any More | Identities for Related Angles

Solving Triangles: Law of Sines | Law of Cosines | Detective Work: Solving All Types of Triangles

The “Squared” Identities

Sum and Difference Formulas: Sine and Cosine of A±B | Tangent of A±B | Product-Sum Formulas

Double Angle and Half Angle Formulas: Sine or Cosine of a Double Angle | Tangent of a Double Angle | Sine or Cosine of a Half Angle | Tangent of a Half Angle

Inverse Functions: Principal Values | Functions of Arcfunctions | Arcfunctions of Functions

Notes and Digressions: The Problem with Memorizing | Proof of Euler’s Formula | Polar Form of a Complex Number | Powers and Roots of a Complex Number | Logarithm of a Negative Number | Cool Proof of Double-Angle Formulas | Great Book on Problem Solving | What’s New

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